Math & Kinematics

Cartesian Space (Task Space)

Cartesian space, also called task space, is the coordinate space in which end-effector poses are described, typically position in R3 plus orientation, forming the special Euclidean group SE(3). It contrasts with joint (configuration) space, where states are joint angles. Motion goals for manipulation are naturally expressed in task space and mapped to joint space through inverse kinematics or differential kinematics via the Jacobian.

Why it matters for physical AI

Most learned manipulation policies output task-space actions such as end-effector deltas because they transfer more readily across robots with different kinematics than raw joint commands.